The United Nations general secretary, Ban Ki-moon, has appealed for swifter aid to provide immediate relief in food, shelter and clean water for the millions affected by the worst monsoon rains on record.

"Make no mistake, this is a global disaster," Ban told a hurriedly convened session of the UN general assembly. "Pakistan is facing a slow-motion tsunami. Its destructive powers will accumulate and grow with time," he warned.

Weather forecasts have said there could be four more weeks of rain, which will add to the flood problems.

The UN has appealed for $460m (£295m) in aid and donors have so far given about half that figure. But the secretary-general said all of the money was needed immediately to help victims over the next three months.

The US has pledged an extra $60m in help, bringing America's total aid to $150m.

In a video message, US secretary of state Hillary Clinton appealed to the American public to donate generously to a newly established "Pakistan relief fund".

"The enormity of this crisis is hard to fathom, the rain continues to fall and the extent of the devastation is still difficult to gauge," said Clinton. "Our thoughts and prayers are with those who have lost loved ones, those who have been displaced from their homes and those left without food and water."

The US special representative for Pakistan, Richard Holbrooke, said "many billions" would be needed to respond to the flooding. Speaking at the Asia Society in New York, he called on other countries, such as China, to step up to the plate and said: "The water has affected everyone, It's an equal opportunity disaster, and military operations have effectively faded away."

The British government yesterday pledged to double its emergency payments, raising its pledge to £64.3m.

Last weekend, one of the UK's funds for disasters – the CERF – was included in a list of items sent by DFID's director of policy to international development secretary Andrew Mitchell as possibly expendable. His department insists the list was only a speculative part of due process, since the department, like all others, is expected to consider value for money, despite DFID being ringfenced from cuts.

But tonight Mitchell, who has recently visited Pakistan to inspect the effect British aid has had so far, told the UN general assembly in New York that the international community had to do more. He told the UN it was "deeply depressing" that the international community was "only now waking up to the true scale of this disaster".

Mitchell will meet other development secretaries and push them to give more. He emphasised funding would only be allocated to NGOs and UN agencies which could prove they were helping people get back on their feet.

He highlighted a fund that would give farmers new seed to plant new crops to replace those destroyed by the floods as a project the UK would back.

He said: "I've come to New York directly from Pakistan, where I saw the dire need for more help. I saw the sheer and shocking magnitude of this catastrophe. It is clear that unless more aid is delivered now, many more people will die from disease and malnutrition. The UK is already helping more than three million people in flood-affected areas." This doubling of our aid should now provide water and sanitation to 500,000 people; shelter to 170,000 people; help meet the nutritional needs of 380,000 people and provide enough health services to cover a population of 2.4 million people."